We call a group $G$ belongs to the class of groups $S_{p}'$, if for every $pd$-chief factor $A/B$ $G$, $((A/B)_{p})'=1$. In this paper, we investigate influence some second maximal subgroups which are related non-$c_{p}$-normal on structure $S_{p}'$.

In this paper, we show that the causally connected $4$-dimensional line element of $\kappa$-deformed Minkowski space-time induces an upper cut-off on proper acceleration and derive maximal acceleration, valid up to first order in deformation parameter. We find a contribution which is independent $\hbar$ thus signals effect non-commutativity alone. also construct geodesic equation obtain its New...